Investigation of floor Nusselt number in floor heating system for insulated ceiling conditions

In this study, in a floor heated room, natural convection heat transfer over the floor is analysed numerically for different thermal conditions. An equation relevant to Nusselt number over the floor has been obtained by using the numerical data. Different equations are given in the literature. They consider the effect of floor Rayleigh number while neglecting the effect of wall and ceiling thermal conditions. Numerical data obtained in this study show that the Nusselt number over the floor depends on not only the floor Rayleigh number but also the wall Rayleigh number (for insulated ceiling conditions). The equations given in the literature are different from each other due to their not considering the effect of wall and ceiling Rayleigh numbers. This difference between the equations may be eliminated by obtaining an equation containing the effect of floor, wall and ceiling Rayleigh numbers. In this new approach, an equation relevant to the floor Nusselt number that depends on the floor and wall Rayleigh numbers has been obtained in the floor heating system for insulated ceiling conditions. The equation obtained in this study has been compared with the equations given in the literature. It has been seen that the equation obtained in this study matches the numerical values under more extensive thermal conditions than the equations given in the literature. The maximum deviation for the equations given in the literature is 35%, but in the current study, the maximum deviation has been found to be 10%. As a result, it is more convenient to use the equation found in the new approach as a function of Rayleigh number over the floor and wall for insulated ceiling conditions.